Detector channel gain calibration using focal spot wobble

ABSTRACT

A 3rd generation CT system produces gain calibration factors (γ) for each channel of a detector array while a scan is being performed. Redundant views are acquired during the scan but the x-ray intensity values in the second view are shifted to the adjacent detector channel by focal spot wobbling the x-ray source. Gain calibration factors (γ) are calculated using the ratio (β) of x-ray intensity values measured at adjacent detector channels.

BACKGROUND OF THE INVENTION

The present invention relates to computed tomography (CT) imagingapparatus; and more particularly, to the calibration of the x-raydetector channels.

In a current computed tomography system, an x-ray source projects afan-shaped beam which is collimated to lie within an X-Y plane of aCartesian coordinate system, termed the "imaging plane." The x-ray beampasses through the object being imaged, such as a medical patient, andimpinges upon an array of radiation detectors. The intensity of thetransmitted radiation is dependent upon the attenuation of the x-raybeam by the object and each detector produces a separate electricalsignal that is a measurement of the beam attenuation. The attenuationmeasurements from all the detectors are acquired separately to producethe transmission profile.

The source and detector array in a conventional "3rd generation" CTsystem are rotated on a gantry within the imaging plane and around theobject so that the angle at which the x-ray beam intersects the objectconstantly changes. A group of x-ray attenuation measurements from thedetector array at a given angle is referred to as a "view" and a "scan"of the object comprises a set of views made at different angularorientations during one revolution of the x-ray source and detector. Ina 2D scan, data is processed to construct an image that corresponds to atwo dimensional slice taken through the object. The prevailing methodfor reconstructing an image from 2D data is referred to in the art asthe filtered backprojection technique. This process converts theattenuation measurements from a scan into integers called "CT numbers"or "Hounsfield units", which are used to control the brightness of acorresponding pixel on a cathode ray tube display. The accuracy of thisreconstruction is dependent on consistent attenuation measurements ofthe x-rays by the detector elements throughout the scan. Changes indetector gain produce ring artifacts in the reconstructed image.

The gain stability of various x-ray detector materials and associatedelectronics can vary considerably. The gains of the individual detectorchannels in a 3 rd generation CT system are periodically calibrated byperforming an "air scan" in which the x-rays unattenuated by an objectare measured. System integrity depends on a relatively stable gainbetween these periodic calibrations. 0n the other hand, because thedetectors receive unattenuated x-rays during each scan of an object in a4th generation CT system, the detector channel gains can be recalibratedduring each scan. As a result, some attractive x-ray detector materialslike CdTe or CdW0₄ may perform in 4 th generation CT systems but havelimited use in 3 rd generation systems because of their gaininstability.

SUMMARY OF THE INVENTION

The present invention relates to a method for calibrating the detectorchannels on a CT system during a scan in which the x-rays are attenuatedby an object. More specifically, a scan is conducted in which each viewis acquired twice, but the gantry is moved and the x-ray tube focal spotposition is changed between each redundant pair of view acquisitionssuch that the rays are shifted to the next detector in the detectorarray. The relative values of adjacent detector element readings arethen employed to calculate gain calibrations for each detector channelrelative to a reference detector channel.

A general object of the invention is to calibrate detector channel gainduring each scan of an object. By moving the gantry and wobbling thefocal spot the identical ray through the object is measured with twoadjacent detector elements. The readings should be the same and anydifference represents an incremental change in gain between the twochannels. These incremental changes are accumulated throughout thedetector array to arrive at absolute gain calibration corrections foreach detector channel with respect to a reference detector channel.

Another object of the invention is to enable x-ray detector materialswith less stable gain to be used in x-ray CT systems. The gaincalibration changes can be calculated after each pair of redundant viewsis acquired and used to correct data acquired during the next pair ofredundant views. Preferably, however, gain calibration changes will bemeasured over a time interval consistent with the gain stabilitycharacteristics of the particular detector material being used.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pictorial view of a CT imaging system in which the presentinvention may be employed;

FIG. 2 is a block schematic diagram of the CT imaging system;

FIG. 3 is an electrical block diagram of an image constructor whichforms part of the CT system of FIG. 2; and

FIGS. 4A and 4B are schematic diagrams showing how redundant x-ray beamsare produced for adjacent detector elements by rotating the gantry andchanging the tube focal spot.

GENERAL DESCRIPTION OF THE INVENTION

Referring particularly to FIG. 4A, the CT system according to thepresent invention consists of an iso-centric detector array 16 and anx-ray source 13 with two well defined focal spot positions P₂ and P₂with a spatial separation in the scan plane. The two focal spots P₁ andP₂ are activated in an alternating fashion, with only one active at anygiven time during the x-ray exposure, producing twice the number ofviews as compared to a standard CT system. The physical distance betweenthe two focal spots is the equivalent of a gantry rotation correspondingto the displacement by one detector channel 18 in the detector array 16.The mode of operation is then as follows. Starting with an x-ray beamemanating from focal spot position P₁ detector element N produces anoff-set corrected signal

    I.sub.N =α.sub.N * I                                 (1)

with I being the incident x-ray intensity and α_(N) the detector gainfactor. The gantry rotates in the direction indicated by arrow 8 to aposition where element N+1 takes the same position as element N in theprevious view, and the focal spot P₂ moves into the same position as P₁in the previous view. An x-ray beam is produced from focal spot positionP₂ as shown in FIG. 4B, allowing detector element N+1 to see the exactsame x-ray path as element N in the previous view. Assuming a uniformbeam intensity in time, the same intensity (I) will now be incident ondetector channel N+1 producing the detector reading

    I.sub.N+1 =αN.sub.+1 * I.                            (2)

The ratio of two adjacent detector readings from this redundant pair ofviews will thus be given by the ratio of the two gain factors (α_(N) andα_(N+1)) for any two neighboring detector cells:

    I.sub.N /I.sub.N+1 =α.sub.N /α.sub.N+1 =β.sub.N "relative gain factor"                                              (3)

These relative gain factors can be propagated through the entire arrayof M detector elements 18 to provide a gain calibration of the entirearray 16 relative to a single reference detector at the edge of thearray.

Let detector element M be the reference channel, the channel gaincalibration γ_(N) relative to M for all channels may be derived in thefollowing way: ##EQU1##

For any detector element N in the array 16, the gain calibrationreferenced to the end element M may thus be expressed as follows:##EQU2## After applying these gain calibration factors γN to eachdetector cell (N=1, 2, . . . M-1), the two redundant, and correctedreadings may be summed together in order to preserve the same photonstatistics as in a standard CT scan, without having to increase thex-ray source output power. For the next pair of redundant views thefocal spot is deflected back to the original position P₁ and the processrepeats itself.

This procedure enables one to get the same number of gain calibrationsas there are number of views in a standard CT scan (approx. 1000).However, photon statistics in each pair of redundant view readingsdetermine how many views will be combined in order to derive astatistically significant gain calibration factor for each of thedetector cells 18. This procedure will at least allow one gaincorrection per scan, which is similar to the gain corrections currentlyachieved by 4 th generation CT systems.

A refinement of this method is to propagate the relative gain factorβ_(N) to reference detectors at both ends of the array 16. Any error inone of the relative gain measurements β will propagate through to allsubsequent calculations and deterministic errors will accumulate, Theseerrors can be reduced by referencing each detector channel gaincalibration to detector elements 18 at both ends of the array 16. Thus,in addition to referencing the detector channel gain factor α_(N) to theend element gain factor α_(M) as expressed above in equation (4), thedetector channel gain factor α_(N) can be referenced to the firstelement in the array 16 as follows ##EQU3## and therefore; ##EQU4## Theratio between end detector channel gains α₁ /α_(M) is known because theyreceive the same unattenuated intensity I, and another gain calibrationfactor γ_(N) ' can thus be calculated: ##EQU5## γ_(N) and γ_(N') haveessentially independent noise since they are calculated from differentintensity ratios. Also, since the β's are in the numerator in equation(4) and in equation (7) they are in the denominator, the deterministicerrors are opposite in sign. Further, for small N γ_(N) is a betterestimate of the gain calibration than γ_(N) ' since fewer β's contributeto its computation whereas the opposite is true for large N. If it isassumed that all the β's are off by a factor c, then:

    γ.sub.N =γ.sub.N,true C.sup.M-N                (8)

while

    γ.sub.N '=γ.sub.N,true C.sup.-N                (9)

Then,

    [(γ.sub.N).sup.N (γ.sub.N ').sup.M-N ].sup.1/M =γ.sub.N,true                                       (10)

is an unbiased estimate of γ_(N),true. For small c and small noisecontent, an arithmetic weighting as follows

    γ.sub.N,true =(N/M)γ.sub.N +((M-N)/M)γ.sub.N '(11)

also works well. These weightings also reduce the statistical noise inthe measurement as well.

In many cases it is not necessary to measure the absolute gain relativeto one reference channel. Instead, the so-called channel-to-channelgain, the gain of one channel normalized to some average of nearbydetector channels, is preferred. This is essentially a high passfiltered version of γ_(N) which can be computed by high pass filteringthe results of equations (4), (8) or (11) calculated above. In thealternative, the gain changes relative to neighboring detector channelscan be calculated more directly from the set of relative gain factorsβ_(N) by convolving them with a high pass filter kernel as will now bedescribed.

Let ε_(N) be the fractional gain change in channel N since calibration.Thus:

    α.sub.N =a.sub.N (1+ε.sub.N)                 (12)

where a_(N) is the calibrated gain for channel N from the previouscalibration. With this definition, ε_(N) <<1. The rationale for thisapproach is that for small ε, linear expansions should suffice. Thus:##EQU6## Now, defining Δ_(N) to be the difference in fractional gainchange between channels N and N+1, we have: ##EQU7## Note that thepre-calibrated gains appear as ratios. If the detector channels havesimilar enough gain one can assume a_(N) /a_(N+1) =1 and thereby put allthe gain difference into Δ_(N).

What we desire are the ε's. The advantage of obtaining the Δ's from theβ's is that the Δ's are linear in the ε's, in fact the Δ's are simplythe ε's convolved with a filter f=δ(0)-δ(1) where δ is a Dirac deltafunction. Thus, from the Δ's which are computed using equation (14), theε's can be found by convolving with the inverse of f, f⁻¹, and the α'scan be computed using equation (12).

For high passed (channel-to-channel) gain changes we desire theconvolution of the ε's with some high pass filter g. One recognizes thatthe Δ's are already a high passed version of ε; the only problem is thatthe high pass filter f=δ(0)-δ(1) is not necessarily the filter g wewant. It can be shown that the desired high passed gains γ_(N) ^(`) canbe directly computed from the Δ's by a convolution with a filter that isa modified version of the desired high pass filter g. The new filter "k"is in fact one term shorter than g. That is if the desired high passfilter g is a seven point high pass filter kernel (g₃, g₂, g₁, g₀, g₁,g₂, g₃), then the new filter k is a six point high pass filter in whichthe values are calculated as follows:

    k.sub.0 =g.sub.3

    k.sub.1 =g.sub.3 +g.sub.2

    k.sub.2 g.sub.3 +g.sub.2 +g.sub.1

    k.sub.3 =g.sub.3 +g.sub.2 +g.sub.1 +g.sub.0

    k.sub.4 +g.sub.3 +g.sub.2 +2g.sub.1 +g.sub.0

    k.sub.5 =g.sub.3 +2g.sub.2 +2g.sub.1 +g.sub.0

Thus the desired gain adjustments are calculated by convolving the gainchanges between channels Δ_(N) with the filter k:

    γ.sub.N.sup.1 =Δ.sub.N  k                      (16)

The so-called calibration air-scan is not entirely eliminated, when thepresent invention is employed since it is required for CT systems with abow-tie beam filter in order to characterize the bow-tie shape relativeto the two different focal spot positions P₁ and P₂. The bow-tie filtercauses a difference in the incident x-ray flux (I) for the two adjacentreadings I_(N) and I_(N+) ₁ due to different x-ray path lengths throughthe bow-tie filter. This difference can be characterized by means of anair calibration scan with no object in the scan path. Variations in thex-ray source output flux over time is also corrected by means of areference detector at the end of the array 16 that is exposed to theunattenuated x-ray beam at all times.

DETAILED OF THE PREFERRED EMBODIMENT

With reference to FIGS. 1 and 2, a computed tomography (CT) imagingsystem 10 includes a gantry 12 representative of a "third generation" CTscanner. Gantry 12 has an x-ray source 13 that projects a cone beam ofx-rays 14 toward a detector array 16 on the opposite side of the gantry.The detector array 16 is formed by a number of detector elements 18which together sense the projected x-rays that pass through a medicalpatient 15. Each detector element 18 produces an electrical signal thatrepresents the intensity of an impinging x-ray beam and hence theattenuation of the beam as it passes through the patient. During a scanto acquire x-ray projection data, the gantry 12 and the componentsmounted thereon rotate about a center of rotation 19 located within thepatient 15.

The rotation of the gantry and the operation of the x-ray source 13 aregoverned by a control mechanism 20 of the CT system. The controlmechanism 20 includes an x-ray controller 22 that provides power, timingsignals, and focal spot position control for the x-ray source 13 and agantry motor controller 23 that controls the rotational speed andposition of the gantry 12. A data acquisition system (DAS) 24 in thecontrol mechanism 20 samples analog data from detector elements 18 andconverts the data to digital signals for subsequent processing. An imagereconstructor 25, receives sampled and digitized x-ray data from the DAS24 and performs high speed image reconstruction according to the methodof the present invention. The reconstructed image is applied as an inputto a computer 26 which stores the image in a mass storage device 29.

The computer 26 also receives commands and scanning parameters from anoperator via console 30 that has a keyboard. An associated cathode raytube display 32 allows the operator to observe the reconstructed imageand other data from the computer 26. The operator supplied commands andparameters are used by the computer 26 to provide control signals andinformation to the DAS 24, the x-ray controller 22 and the gantry motorcontroller 23. In addition, computer 26 operates a table motorcontroller 34 which controls a motorized table 36 to position thepatient 15 in the gantry 12.

Referring particularly to FIG. 3, as each view is acquired during a scana set of scan data values which indicate the number of x-ray photonssensed by the detector elements 18 are conveyed by the DAS 24 to theimage constructor 25. These intensity values I are produced by thedetectors 18 and are subject to changes in detector channel gain whichmust be corrected along with other errors in a correction circuit 41.The intensity values are thus applied through a bus 42 to the correctioncircuit 41 which adjusts the scan data for variations in detector andDAS channel gains, dark current offsets and beam hardening. The samescan data is also conveyed through bus 42 to a gain calibration circuit43 which executes the above described equations (4), (7) and

(10) to produce gain calibration values γ_(N) to the correction circuit41. After correction by the circuit 41, corrected scan data fromredundant pairs of views is combined at summing circuit 44 and theresulting scan data is processed in a well known manner by taking thenegative of its logarithm at 45 to produce a single projection profilefor each view. These projection profiles are applied to a reconstructionprocessor 46 which filters and back projects them to form slice imagesthat are output at 47 to the computer 26.

The gain calibration circuit 43 makes its calculations as describedabove to produce a set of gain calibration factors γ_(N) after each pairof redundant views are acquired during the scan. While these valuesγ_(N) can be applied to the correction circuit 41 and used to change thegain corrections made to each pair of redundant views, in the preferredembodiment the sets of values γ_(N) are examined and combined to formthe best estimate of the true gain ratios, new gain calibration factorsγ_(N) are output to the correction circuit 41.

It should be apparent to those skilled in the art that many variationscan be made from the preferred embodiments described above withoutdeparting from the spirit of the invention. For example, the detectorarray in the preferred embodiment is concentric, or centered, about theaxis of rotation 19. The invention may also be employed in systems wherethe detector array is concentric about the focal spots in the x-ray tube13, as long as the arc subtended by the detector array is not too large.

We claim:
 1. In a CT system having an x-ray source which is revolvedaround an object to be imaged and a detector array comprised of a set ofdetector channels for producing a corresponding set of x-ray intensityvalues at each of a succession of views as the x-ray source revolves, amethod for producing detector channel gain calibration factors (γ), thesteps comprising:a) acquiring a first set of x-ray intensity values withx-rays emanating from a first focal spot position (P₁) in the x-raysource; b) rotating the x-ray source to a position for acquiring thenext view of the object; c) acquiring a second set of x-ray intensityvalues with x-rays emanating from a second focal spot position (P₂) inthe x-ray source which is displaced in the plane of x-ray sourcerevolution such that the second set of x-ray intensity values areredundant of the first set of x-ray intensity values; d) calculating therelative gain factor (β) of adjacent detector channels by taking theratio of the x-ray intensity values acquired in steps a) and c); and e)calculating a gain calibration factor (γ) for each detector channelwhich relates the gain of said detector channel to a reference detectorchannel in the detector array using the relative gain factors (β)calculated in step d).
 2. The method as recited in claim 1 in which thedetector array revolves around the object along with the x-ray source.3. The method as recited in claim 1 in which the reference detectorchannel is located at one end of the detector array
 16. 4. The method asrecited in claim 1 in which the gain calibration factor (γ) calculatedin step e) also relates the gain of each detector channel to a secondreference detector channel located at a second end of the detector arrayusing the relative gain factors (β) calculated in step d).
 5. The methodas recited in claim 1 in which steps a), b) and c) are repeatedthroughout the revolution of the x-ray source around the object toacquire a redundant set of x-ray intensity values at each view of theobject.
 6. In a CT system having an x-ray source which is revolvedaround an object to be imaged and a detector array comprised of a set ofdetector channels for producing a corresponding set of x-ray intensityvalues at each of a succession of views as the x-ray source revolves, amethod for producing detector channel gain calibration factors (γ), thesteps comprising:a) acquiring a first set of x-ray intensity values withx-rays emanating from a first focal spot position (P₁) in the x-raysource; b) rotating the x-ray source to a position for acquiring thenext view of the object; c) acquiring a second set of x-ray intensityvalues with x-rays emanating from a second focal spot position (P₂) inthe x-ray source which is displaced in the plane of x-ray sourcerevolution such that the second set of x-ray intensity values areredundant of the first set of x-ray intensity values; d) calculating thedifference in gain changes (Δ) between adjacent detector channels bytaking the ratio of the x-ray intensity values acquired in steps a) andc); and e) calculating a gain calibration factor (γ) for each detectorchannel by convolving the difference in gain change values (Δ) with afilter kernel k.